The spectral bundle method has turned out to be a useful algorithmic tool to approximately solve SDP having the constant trace property, i.e. A(X)=b implies that trace(X) is constant.
We will review this method in the general setting of bundle methods, and also in the context of second order methods for eigenvalue optimization. While a clean second order method for eigenvalue optimization has no immediate advantage over interior-point methods, this approach can still be used to generate a diagonal scaling matrix for the prox-term in the bundle method to improve convergence, once close to the optimum.
We present the relevant mathematical background, the basic convergence results and explain the main computational steps. It turns out that an eigenvalue decomposition is necessary in each iteration, but no other high level matrix operations.
Last modified: Mon Sep 23 18:53:51 CEST 2004